This study was to support the understanding of the set structure, binary operations, and their properties as a prerequisite of group theory material categorized as 9 structure senses. This study aimed at investigating the process of students’ structure sense in recognizing the structure of mathematical properties or objects as a prerequisite of group theory material. A task-based case study by exploring 9 categories of structure senses through three integrated process frameworks in the questionnaire was employed in this study. It involved 26 students who had obtained a prerequisite of group theory material and would take abstract algebra course. The choice of subjects was determined based on the results of the questionnaire, in which it identifies the type of structure sense processes. There were 6 out of 26 subjects were chosen. The 6 subjects consisted of 2 subjects from the first path process, 2 subjects from the second path process, and 2 subjects from the third path process. Then, the 6 subjects were interviewed. The choice of 2 subjects for each path process was because it used a fixed comparison theory. Then, the data were validated by using triangulation methods by comparing the students’ work on assignments and questionnaires as well as audio recordings of interviews. The results show the tendency of the process of structure sense was more dominated by students from the second type of path process, in which the subjects still depend on the well-known structure of the properties or mathematical objects in the form of sample questions. The subjects were unable to understand definitions in order to construct structures of properties or mathematical objects.

This research aimed at analyzing the influence of ‘Process Oriented Guided Inquiry Learning’ model assisted by realia media, in which it was to improve the scientific literacy and critical thinking skill of primary school students, especially for the material of energy. This quasi-experiment research used single factor independent groups design. The research sample of this research were fourth grade students of SD Inpres Oeba 2 Kupang City, East Nusa Tenggara Province, of which students were in the academic year of 2019/2020. The technique of sample collection was carried out purposive sampling for 2 classes. The IVA class was used as the experimental class (POGIL model assisted by the realia media), in which it consisted of 30 students and the IVB class was used as the control class (expository learning) that consisted of 28 students. The learning was carried out in four meetings. The data of scientific literacy and the results test of critical thinking were collected by means of objective test on the energy material. Multivariate Analysis of Variance (MANOVA) was used to analyze the data using significance level of 0.05. The results indicate that (1) There is a significant difference between the students’ scientific literacy who gain the POGIL learning assisted by the realia media and the students’ scientific literacy who get the expository learning; and (2) There is a significant difference between the critical thinking of students who get POGIL learning assisted by realia media and the students who get the expository learning. It can be concluded that there is a significant difference between the scientific literacy and the students’ critical thinking taught by the POGIL learning that assisted by realia media to the students who use expository learning. Since there is a significant difference, it means that the POGIL learning assisted by realia media has an influence on the students' scientific literacy and critical thinking.

Students' critical thinking ability requires improvement from schools as an educational institution. Besides, it is important to maximally integrate character education into mathematics learning. One of the attempts was implementing mathematics comic that contains Pancasila values as teaching material through contextual teaching and learning. Therefore, this study aims to analyze the effectiveness of mathematics comic teaching material with Pancasila values in improving students' critical thinking and character. This is a quasi-experimental study that involves non-equivalent control group design. The population was fourth-grade students of elementary schools in Gajahmungkur District, and data were collected using a critical thinking test and questionnaire. The results showed that using mathematics comic teaching material with Pancasila values was (1) effective in improving students' critical thinking ability; (2) effective in developing character, especially discipline and hard work trait. In the beginning, both character traits were categorized as good, and after treatment, there was an increase in the very good category. Therefore, it can be concluded that the use of mathematics comic teaching material with Pancasila values is effective in improving critical thinking ability and character traits.

This study aimed to analyze the critical thinking skills of students in learning of environmental change material using e-learning madrasah. This study used explanatory sequential design by mixed-methods experiment. The data were collected by interviewing, observing, and essay testing that have indicators modified from critical thinking skills by Watson-Glaser, Facione, and Ennis. There were 67 participants in this study as 7th grade student at a junior high school in Sleman district. Quantitative data analyzed by determining average score and standard deviations and, qualitative data analyzed from interviews and observation. Quantitative analysis showed that there were 3 levels of student’s critical thinking skills which were 14 students (20.90%) in the high category, 38 students (56.72%) in the middle category, and 15 students (22.38%) in the low category. Qualitative analysis indicated learning model made students to learn actively, independently, and enthusiastically looking for several sources. This study provided information about student critical thinking skills in junior high school, especially in the environmental change matter which are still low. Thus, the alternative learning strategies to improve students critical thinking skills are very needed. Besides, information on the application of the discovery learning model with e-learning Islamic school was obtained in the COVID-19 pandemic.

This study investigated the effectiveness of visual mind mapping as a reading strategy for improving English language learners' critical thinking skills. Students from two general English courses were randomly assigned to experimental and control groups. California Critical Thinking Test was used to assess participants' critical thinking skills. The findings revealed a statistically significant difference at (p < .005) in the mean scores of the experiment and control groups in the post-test due to visual mind mapping strategy in favor of the experimental group with a positive and significant impact on participants' critical thinking skills. The findings also showed that the experimental group’s scores were significantly improved in all indicators of critical thinking. The study results showed that visual mind mapping strategy affected the increased of critical thinking skills and reading comprehension ability. The study's findings revealed that using a visual mind mapping strategy had a significant improvement impact on English language learners critical thinking skills and reading ability.

The skill to solve mathematical problems facilitates students to develop their basic skills to solve problems in daily life. This study analyzes students' problem-solving process with a reflective cognitive style in constructing probability problems using action, process, object, and schema theory (APOS). The explanatory method was used in this qualitative study. The participants were mathematics students at the Department of Mathematics, Universitas Negeri Semarang. The researchers collected the data with the cognitive style test using the Matching Familiar Figure Test (MFFT), used a valid problem-solving skill test, and the interview questions. The data analysis techniques used were processing and preparing the data for analysis, extensive reading of the data, coding all data, applying the coding process, describing the data, and interpreting the data. The results showed that (1) the problem-solving process of students with symbolic representation was characterized by the use of mathematical symbols to support the problem-solving process in the problem representation phase; (2) the problem-solving process of students with symbolic-visual representation was characterized by the use of symbols, notations, numbers, and visual representation in the form of diagrams in the problem representation phase.

This study is qualitative with descriptive and aims to determine the process of generalizing the pattern image of high performance students based on the action, process, object, and schema (APOS) theory. The participants in this study were high performance eighth-grade Indonesian junior high school. Assignments and examinations to gauge mathematical aptitude and interviews were used to collect data for the study. The stages of qualitative analysis include data reduction, data presentation, and generating conclusions. This study showed that when given a sequence using a pattern drawing, the subjects used a number sequence pattern to calculate the value of the next term. Students in the action stage interiorize and coordinate by collecting prints from each sequence of numbers in the process stage. After that, they do a reversal so that at the object stage, students do encapsulation, then decapsulate by evaluating the patterns observed and validating the number series patterns they find. Students explain the generalization quality of number sequence patterns at the schema stage by connecting activities, processes, and objects from one concept to actions, processes, and things from other ideas. In addition, students carry out thematization at the schematic stage by connecting existing pattern drawing concepts with general sequences. From these results, it is recommended to improve the problem-solving skill in mathematical pattern problems based on problem-solving by high performance students', such as worksheets for students.